caa a22 4500 445361468 CHVBK 20180317142916.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s11071-010-9873-5 doi (NATIONALLICENCE)springer-10.1007/s11071-010-9873-5 Time-fractional KdV equation: formulation andsolution using variational methods [Elektronische Daten] [S. El-Wakil, E. Abulwafa, M. Zahran, A. Mahmoud] In this work, the semi-inverse method has been used to derive the Lagrangian of the Korteweg-deVries (KdV) equation. Then the time operator of the Lagrangian of the KdV equation has been transformed into fractional domain in terms of the left-Riemann-Liouville fractional differential operator. The variational of the functional of this Lagrangian leads neatly to Euler-Lagrange equation. Via Agrawal's method, one can easily derive the time-fractional KdV equation from this Euler-Lagrange equation. Remarkably, the time-fractional term in the resulting KdV equation is obtained in Riesz fractional derivative in a direct manner. As a second step, the derived time-fractional KdV equation is solved using He's variational-iteration method. The calculations are carried out using initial condition depends on the nonlinear and dispersion coefficients of the KdV equation. We remark that more pronounced effects and deeper insight into the formation and properties of the resulting solitary wave by additionally considering the fractional order derivative beside the nonlinearity and dispersion terms. Springer Science+Business Media B.V., 2010 Riemann-Liouville fractional differential operator nationallicence Euler-Lagrange equation nationallicence Riesz fractional derivative nationallicence Fractional KdV equation nationallicence He's variational-iteration method nationallicence Solitary wave nationallicence El-Wakil S. Theoretical Physics Research Group, Physics Department, Faculty of Science, Mansoura University, 35516, Mansoura, Egypt aut Abulwafa E. Theoretical Physics Research Group, Physics Department, Faculty of Science, Mansoura University, 35516, Mansoura, Egypt aut Zahran M. Theoretical Physics Research Group, Physics Department, Faculty of Science, Mansoura University, 35516, Mansoura, Egypt aut Mahmoud A. Theoretical Physics Research Group, Physics Department, Faculty of Science, Mansoura University, 35516, Mansoura, Egypt aut Nonlinear Dynamics Springer Netherlands 65/1-2(2011-07-01), 55-63 0924-090X 65:1-2<55 2011 65 11071 https://doi.org/10.1007/s11071-010-9873-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9873-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- El-Wakil S. Theoretical Physics Research Group, Physics Department, Faculty of Science, Mansoura University, 35516, Mansoura, Egypt aut NATIONALLICENCE 700 1- Abulwafa E. Theoretical Physics Research Group, Physics Department, Faculty of Science, Mansoura University, 35516, Mansoura, Egypt aut NATIONALLICENCE 700 1- Zahran M. Theoretical Physics Research Group, Physics Department, Faculty of Science, Mansoura University, 35516, Mansoura, Egypt aut NATIONALLICENCE 700 1- Mahmoud A. Theoretical Physics Research Group, Physics Department, Faculty of Science, Mansoura University, 35516, Mansoura, Egypt aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 65/1-2(2011-07-01), 55-63 0924-090X 65:1-2<55 2011 65 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer